Grain boundary solute drag

Figure 13.6 Grain-boundary solute-drag phenomena predicted by Cahn s model, (a)...

The effect of solute atoms on grain boundary migration cannot adequately be described by standard impurity drag theories. A more satisfactory agreement is obtained by taking an interaction ofthe impurities in the boundary into account. 

In solution drag, the width of the grain bovmdaiy, w, is the zone over which impurities interact. The grain boimdary thickness is taken to be independent of grain size. The diffusion coefficients of the host, D , and the impvirity, D/, will depend on the structure in the grain boundary. Impurities can therefore have an effect on the grain boundary velocity, Vg, by either their effect on the Co term or an effect on the diffusion coefficients for host and impurity. 

The boundary mobility Mb is determined by the difiusion coefficient Da for the atomic migrates across the grain boundary of the pure material, which is called intrinsic boundary mobility. In ionic solids, because both cations and anions could diffuse, Da is the difiusion coefficient of the species that are rate-limiting or lowest. In real ceramics, various drag forces, such as segregated solutes, inclusions, pores, and second-phase films, can be applied to the grain boundary. As a result, experimental boundary mobility is lower than the Mb given by Eq. (8.30) in most cases. 

Fig. 8.26 Sketch of the solute drag effect produced by the segregation of dopants to the grain boundaries, a Symmetrical distribution of the dopant in the region of a stationary grain boundary, b For a moving boundary, the dopant distribution becomes asymmetrical if the diffusion coefficient of the dopant atoms across the boundary is different from that of the host atoms. The as5nnmetrical distribution produces a drag on the boundary, c Breakaway of the boundary from the dopant leaving a solute cloud behind. Reproduced with permission from [4]. Cop5urght 2003, CRC Press...

The effects of a grain size distribution and solute drag have also been incorporated into the basic model [109, 110]. The critical density at which pore separation occurs is significantly lower for the powder compacts with a wide distribution of particle size than for the powder with a narrow size distribution. Separation of only a fraction of the pores from the boundary is sufficient to cause AGG, which is different from the assumption in the simple analysis that aU pores should separate from the boundaries. 

Hillert M, Sundman B (1976) Treatment of solute drag on moving grain-boundaries and phase interfaces in binary-alloys. Acta Metall 24 731—743... 

Experimental evidences of specific ion or solute segregation and its effect on grain boundary mobility are abundant, as introduced in Section 7.2. With the segregation of solute ions, the boundary velocity can decrease considerably as a result of solute drag within a low velocity limit described in Chapter 7. Segregation of a specific ion species with an electric charge was further confirmed in a recent investigation on the effect of an electric field on... 

Models for grain boundary migration controlled by solute drag have been developed by Cahn (61), Stuwe (62), Hillert and Sundman (63), and others. We shall outline the model of Cahn which is more quantitative and concise than the others and has the advantage that the boundary mobility can be more directly related to the physical parameters of the process. The model analyzes the problem in one dimension and makes the following assumptions ... 

Physically, a is the solute drag per unit velocity and per unit dopant concentration in the low boundary velocity limit, whereas 1/p is the drift velocity with which an impurity atom moves across the grain boundary. From the form of Eq. (9.67), solutes with either an attractive or repulsive interaction energy of the same magnitude will exert a similar drag force. 

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